Hilbert Space

こんにちは

時系列解析で、ARMAモデルを学習していました。必ずHilbert SpaceでのProjection Theorem に出くわします。どうして、Hilbert Space　なのか、ということが理解しにくいのです。時系列のtrend が有限で一般的な級数展開で表現されるとのことですか、いつもこれが成り立つとは限らないところに、Hilbert Space Theoremの必要性があると感じています。しかしながら、Hilbert Space Theorem 自身理解することが困難です。とりくんでいるかたがいらっしゃれば、ご教示いただきたいと思います。

Hollow, I have investigated ARMA model regarding Time Series Analysis. I am sure to encounter understanding of Projection Theorem in Hilbert Space. It is difficult for me to understand how ARMA model needs the environment in Hilbert Space. Though I understand the Time Series Trend can be represented by a defined general power series development, the appropriate power series doesn’t always exist against that. So that I suppose it needs Hilbert Space Theorem as stated above. If there are those who come to grips with this problem, I would like to teach me about that. Sincerely.